At present, in order to meet the needs of the complex nonlinear system control, many model-based control algorithms have been proposed (such as model predictive control, robust control, nonlinear control, optimal control, etc.), but there exists one very important factor to restrict the wider applications of these control algorithms, which is the need for accurate and reliable nonlinear models with limited identification data. In the field of nonlinear identification, identification of nonlinear or linear parameter varying models has been the research hotspot.
In the field of nonlinear identification, there are three main types of identification methods: the first type is the piecewise linear methods for weak nonlinear system identification; the second type is the non-parametric model identification methods, mainly including neural networks identification method and fuzzy identification method; the third type is the system identification methods based on Hammerstein or Wiener model structure, which comprise the static nonlinear part and the dynamic linear part, and they have been widely used in the field of nonlinear identification. The above nonlinear identification methods are identification methods based on constant parameters (i.e. constant operating point variable values). However, in the real industries, the model identification based on varying parameters will bring great improvements for the controller design optimization.
In recent years, the identification research of linear parameter varying models has achieved great progress. The identification concept of linear parameter varying models (Linear Parameter Varying, or LPV for short) was first proposed by the Shamma and Athans, where the system is described by linear models with varying parameters. The main directions of this field can be divided into two categories: one is based on the parameter interpolation LPV models, and the other is based on model interpolation LPV models. As pointed out in the literature of Yu Zhao et al. (2011), Prediction error method for identification of LPV models, Journal of Process Control, 22(1):180-193, the model interpolation LPV model identification method is better than the parameter interpolation LPV model identification method in both computation time and accuracy. Although the linear parameter varying models can be a good solution to describe the effect of parameter nonlinear varying on the system, they uses simple linear models to describe the system models at a given operating point, ignoring the nonlinear relationship between the system input and the system output at a given operating point. However, in the real industrial process, there exists not only the nonlinearity of parameter varying, but also the nonlinearity between the system input and the system output at a given operating point.
Thus, it is of great significance for model-based control to propose a model identification method taking into account both the nonlinearity between the system input and the system output at a given operating point and the nonlinearity of parameter varying with operating point variable values, meanwhile the method needs limited data for identification and achieves higher accuracy.